Quantification of the Contribution of the Different Components Concerning Two-Phase Flow in Heterogeneous Porous Media

Abstract

Abstract Two phase flow through heterogeneous porous media can be divided in ‘convective’ and ‘diffusive’ flow processes. The ‘convective’ part consists of the flow behaviour due to the large scale permeability field variations and an additional ‘two phase’ part generally captured in relative permeabilities. The ‘diffusive’ process is generally captured in the capillary pressure formulation. In this study we express the two phase flow behaviour as a convolution between the multidimensional single phase (tracer) flow behaviour with the one-dimensional two phase flow behaviour. For Piston like flow through a more dimensional heterogeneous medium, the velocity field remains constant during flooding and one can divide the flow field in constant ‘one-dimensional’ streamtubes, see Lenormand (1995). Under the assumption that the variation in streamtubes through the same field during two-phase flooding is negligible one can express the watercut profile of two phase flow in the watercut profile for Piston like flow convolved with the Buckley Leverett saturation profile. In this study we compute the Piston like flow through three different permeability fields (one homogeneous field and two heterogeneous fields with an omni-directional correlation length of 0.5 respectively 0.95). We calculate 4 different two-phase flow behaviours by means of convolution and compare this to fully two dimensional flow simulations performed with an in house developed streamline simulator. We define a measure - based on the difference between Piston like and Buckley Leverett production - to quantify and characterise each different two-phase flow type. It appears that the convolved two phase flow behaviour shows a reasonable estimate of the fully two-phase flow behaviour, although the difference in the two dimensional total mobility distribution can affect the moment of breakthrough considerably. The defined production measure appears to show similar results for both the convolved and fully simulated two phase displacements. The benefit of the convolution method is that with only a single high resolution Piston like displacement numerous different two phase flow displacements can be estimated very cheaply.